Final answer:
To solve the equation 1+cot² (−α)/csc³α=12, simplify the trigonometric expressions and manipulate the equation to solve for α.
Step-by-step explanation:
To solve the equation 1+cot² (−α)/csc³α=12, we need to manipulate the trigonometric expressions and simplify the equation.
First, we'll simplify the cot² (−α) and csc³α terms by using the reciprocal identities: cot(−α) = -cot(α) and csc(α) = 1/sin(α).
Substituting these identities into the equation, we get 1 + (-cot(α))² / (1/sin³(α)) = 12.
Next, we'll simplify the equation by combining like terms and applying trigonometric identities. Finally, we'll solve for α.